The spectral density function for the Laplacian on high tensor powers of a line bundle

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For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density function. We give an explicit computation of the spectral density function, by constructing certain quasimodes on the associated principle bundle.
AMS-Latex, 17 pages

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Spectral Theory, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/61069

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0103062
 http://arxiv.org/abs/math/0103062

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arXiv